Question 915396
They are similar, so the heights are in the same ratio.


The ratio for radius of larger to smaller cone is {{{5/3}}};
and because of the two cones being SIMILAR, the ratio of the HEIGHT of the larger cone to the smaller cone is also {{{5/3}}}.




smaller 3r, 3h
larger, 5r, 5h
Using v for volume of smaller and V for volume or larger,
{{{v=(1/3)(3h)(pi)(3r)^2}}} and {{{V=(1/3)(5h)(pi)(5r)^2}}}.


You can calculate {{{V/v}}}, the ratio of the volume of the larger cone to the volume of the smaller cone.  Substitute the expressions:


{{{((1/3)(5h)(pi)(5r)^2)/((1/3)(3h)(pi)(3r)^2)}}}


Simplify that ratio.